Mathematical DiamondsRoss Honsberger has done it again. He has brought together another wonderful collection of elementary mathematical problems and their solutions abounding in striking surprises and brilliant ideas that reflect the beauty of mathematics. Many of these problems come from mathematical journals. Others come from various mathematical competitions such as the Tournament of the Towns, the Balkan Olympiad, the American Invitational Mathematics Exam, and the Putnam exam. And, of course, there is a problem suggested by Paul Erdös. This book is ideal for students, teachers and anyone interested in recreational mathematics. |
Contents
Preface | 1 |
Apples and Sticks | 9 |
Miscellaneous Gleanings | 19 |
An Application of Turáns Theorem | 35 |
Four Problems from Putnam Papers | 43 |
Topics Based on Problems from Quantum | 49 |
Two Distinguished Integers | 79 |
Nine Miscellaneous Problems | 87 |
Six Problems from the Canadian Open | 117 |
Three Pretty Theorems in Geometry | 125 |
Two Gems from Euclidean Geometry | 135 |
The ThueMorseHedlund Sequence | 143 |
Three Geometry Problems | 169 |
Three Problems From The 1990 Balkan Olympiad | 175 |
A Japanese Fan Problem | 181 |
Slicing a Doughnut | 187 |
A Problem in CoinTossing | 103 |
Semiregular Lattice Polygons | 109 |
A Problem from the 1980 Tournament of the Towns | 195 |
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Common terms and phrases
a₁ AABC ABCD ak+1 algebraic integer altitude an+1 arccos bisects C₁ Ceva's theorem cevian circle circumcenter Clearly coefficients College Mathematics Journal collinear column contains cos˛ countable cyclic quadrilateral determine diagonal diameter distance divide divisible divisor Dolciani doughnut equal equation exceed exponents factor Farey sequence Geometry giving Hence Howard Eves implying isolated points isosceles lattice points lattice polygon length Mathematical Gems medial triangle median midpoint orthic triangle orthocenter pair parallel parallelogram perpendicular plane polynomial positive integer prime number problem proof Prove quadrilateral radius rational recall relatively prime right triangle Ross Honsberger SECTION segment sequence sides Similarly sin˛ solution square-free Stan Wagon subset Suppose switch tangent triangle ABC triples Turán's theorem vertex vertices